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Differential Geometry papers — page 13

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Almost complex structures and geometric quantization
We study two quantization schemes for compact symplectic manifolds with almost complex structures. The first of these is the Spin-c quantization. We prove the analog of Kodaira vanishing for the…
David Borthwick, Alejandro UribeAug 17, 1996
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Gromov-Witten invariants of general symplectic manifolds
We present an approach to Gromov-Witten invariants that works on arbitrary (closed) symplectic manifolds. We avoid genericity arguments and take into account singular curves in the very formulation.…
Bernd SiebertAug 12, 1996
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Pluriharmonic Morphisms
Pluriharmonic maps form an important class of harmonic maps which includes holomorphic maps. We study their morphisms, in particular the inter-relationships between (1,1)-geodesic, pluriharmonic…
Eric LoubeauAug 10, 1996
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Pseudo Harmonic Morphisms
We study a geometrical condition (PHWC) which is weaker than horizontal weak conformality. In particular, we show that harmonic maps satisfying this condition, which will be called …
Eric LoubeauAug 9, 1996
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Higher spectral flow
For a continuous curve of families of Dirac type operators we define a higher spectral flow as a K-group element. We show that this higher spectral flow can be computed analytically by…
Xianzhe Dai, Weiping ZhangAug 8, 1996
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Backlund transformations and knots of constant torsion
The Backlund transformation for pseudospherical surfaces, which is equivalent to that of the sine-Gordon equation, can be restricted to give a transformation on space curves that preserves constant…
Annalisa Calini, Thomas IveyAug 7, 1996
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Diffeomorphisms, Analytic Torsion and Noncommutative Geometry
We prove an index theorem concerning the pushforward of flat B-vector bundles, where B is an appropriate algebra. We construct the associated analytic torsion form T. If Z is a smooth closed…
John LottJul 30, 1996
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Differential operators of Fuchs type, conical singularities, and asymptotic methods
This text is a revised version of the authors Habilitationsschrift which was submitted to the University of Augsburg, 1993. Fuchs type differential operators are used to model the analysis on…
Matthias LeschJul 19, 1996
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Exotic holonomies 7(a)
It is proved that the Lie groups 7(5) and (7)7 represented in 56 and the Lie group 7 represented in 112 occur as holonomies of torsion-free affine connections.…
Q. -S. Chi, S. A. Merkulov, L. J. SchwachhöferJul 18, 1996
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An Intrinsic Approach to Lichnerowicz Conjecture
In this paper we give a proof of Lichnerowicz Conjecture for compact simply connected manifolds which is intrinsic in the sense that it avoids the Nice Embeddings into eigen spaces of the…
Akhil RanjanJul 17, 1996
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The index of operators on foliated bundles
We compute the equivariant cohomology Chern character of the index of elliptic operators along the leaves of the foliation of a flat bundle. The proof is based on the study of certain algebras of…
Victor NistorJul 3, 1996
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Twistor spaces of non-flat Bochner-Kähler manifolds
For the twistor spaces of the Bochner-Kähler manifold M = Hl × Pn, systems of holomorphic coordinates are constructed. As an application of them, an explicit description of the moduli space…
Yoshinari InoueJul 2, 1996
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Combinatorial invariants computing the Ray-Singer analytic torsion
It is shown that for any piecewise-linear closed orientable manifold of odd dimension there exists an invariantly defined metric on the determinant line of cohomology with coefficients in an…
Michael FarberJul 1, 1996
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Homological algebra of Novikov-Shubin invariants and Morse inequalities
It is shown that the topological phenomenon "zero in the continuous spectrum", discovered by S.P.Novikov and M.A.Shubin, can be explained in terms of a homology theory on the category of…
Michael FarberJul 1, 1996
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Hinges and geometric constructions of boundaries of symmetric spaces
We give elementary constructions for Satake-Furstenberg, Martin and Karpelevich boundaries of symmetric spaces. We also consruct some "new" boundaries
Yurii A. NeretinJun 26, 1996
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Analytic fields on compact balanced Hermitian manifolds
On a Hermitian manifold we construct a symmetric (1,1)- tensor H using the torsion and the curvature of the Chern connection. On a compact balanced Hermitian manifold we find necessary and…
George Ganchev, Stefan IvanovJun 24, 1996
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Smooth classification of Cartan actions of higher rank semisimple Lie groups and their lattices
Let G be a connected semisimple Lie group without compact factors whose real rank is at least 2, and let Γ⊂ G be an irreducible lattice. We provide a C∞ classification for…
Edward R. Goetze, Ralf J. SpatzierJun 21, 1996
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On Livsic's Theorem, Superrigidity, and Anosov Actions of Semisimple Lie Groups
We prove a generalization of Livsic's Theorem on the vanishing of the cohomology of certain types of dynamical systems. As a consequence, we strengthen a result due to Zimmer concerning algebraic…
Edward R. Goetze, Ralf J. SpatzierJun 21, 1996
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Novikov inequalities with symmetry
We establish an equivariant generalization of the Novikov inequalities which allow to estimate the topology of the set of critical points of a closed basic invariant 1-form by means of twisted…
Maxim Braverman, Michael FarberJun 20, 1996
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Example of a non-log-concave Duistermaat-Heckman measure
We construct a compact symplectic manifold with a Hamiltonian circle action for which the Duistermaat-Heckman function is not log-concave.
Yael KarshonJun 20, 1996
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Positive paths in the linear symplectic group
A positive path in the linear symplectic group (2n) is a smooth path which is everywhere tangent to the positive cone. These paths are generated by negative definite (time-dependent) quadratic…
Francois Lalonde, Dusa McDuffJun 18, 1996
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Lectures on Gromov invariants for symplectic 4-manifolds
These are notes of lectures given at the NATO Summer School, Montreal 1995. Taubes's recent spectacular work setting up a correspondence between J-holomorphic curves in symplectic 4-manifolds…
Dusa McDuffJun 18, 1996
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From symplectic deformation to isotopy
Let X be an oriented 4-manifold which does not have simple SW-type, for example a blow-up of a rational or ruled surface. We show that any two cohomologous and deformation equivalent symplectic…
Dusa McDuffJun 17, 1996
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Equivariant Seiberg-Witten Floer Homology
This paper circulated previously in a draft version. Now, upon general request, it is about time to distribute the more detailed (and much longer) version. The main technical issues revolve around…
Matilde Marcolli, Bai-Ling WangJun 14, 1996
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Harmonic two-spheres in compact symmetric spaces, revisited
Uhlenbeck introduced an invariant, the (minimal) uniton number, of harmonic 2-spheres in a Lie group G and proved that when G=SU(n) the uniton number cannot exceed n-1. In this paper, using new…
Francis Burstall, Martin GuestJun 14, 1996
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